<PRE><B>Question 195801</B>
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Presuming the tower is exactly vertical and the ground is perfectly level -- an ok assumption in a math word problem, but not necessarily valid in a real life situation -- then you have a right triangle with a hypotenuse of &lt;b&gt;&lt;i&gt;&lt;/i&gt;30&lt;/b&gt;, a short leg of &lt;b&gt;&lt;i&gt;d&lt;/i&gt;&lt;/b&gt;, and a long leg of &lt;b&gt;&lt;i&gt;d&lt;/i&gt; + 6&lt;/b&gt;, so:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ d^2 + (d + 6)^2 = 30^2]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ d^2 + d^2 + 12d + 36 = 900]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2d^2 + 12d - 864 = 0]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ d^2 + 6d - 432 = 0]


So just solve the quadratic for &lt;b&gt;&lt;i&gt;d&lt;/i&gt;&lt;/b&gt;.  Hint:  It factors.  Exclude the negative root because you are looking for a positive measure of length.



John
*[tex \LARGE e^{i\pi} + 1 = 0]
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